Mowing lawn can cost anywhere from $25 to $200 depending on the size of the lawn. Will you mow your lawn if it costed you $10,000? Why is this hypothetical question relevant? I want to explore immigration policies and the impact it has on wages.
Increasing the supply of people with a certain skill set will reduce the price of that skill set in the market. If there are only 5 doctors who could do heart surgeries in the world then the price of a heart surgery will go up to such a level let's say 10 million USD so that those 5 doctors will perform only surgery on people who can afford 10 million USD. Is that a good thing for the doctors? Yes, doctors are likely to prefer to get higher salaries but it will also result in thousands of people dying because there are not enough doctors to perform the number of surgeries needed.
In any economic activity mowing lawn, picking fruit, programming computers or performing surgeries keeping the supply of skilled workers artificially low by strict anti-immigration policies will result in several lawns not being mowed, less fruits being grown, several computer systems not being built or many surgeries not being performed so there's case for immigration of people with the required skill set through legal means. If higher wage is the only interest of workers then they could also wish for the death of people with the same skill set in hope of higher wages. On the other hand allowing people to work in market where there's a higher demand for their skills will increase the total output of the world global GDP and also increase the national GDP as workers can work in countries where they are most productive.
What's the best action for policy makers? Allow legal immigration to industries where there's a shortage of workers. An example would be to allow immigration to an industry where unemployment is less than 5%. What's the best action for workers? Acquire skills that will help them to compete in a global market place of skilled workers.